No. A suite is a very fancy room in a hotel ,but a hotel is a building ,that is usually many stories tall, that contains many rooms in which you can stay for a fee.
If Fall is the same thing as Summer, and there are four seasons, then that would correspond to 7 days of the week, meaning it would actually be closer to Saturday.
Yes, "how do you do?" is a more formal way of saying "how are you?" It is more or less archaic. However, "How do you do" is never responded to literally, by telling the greeter how you are.